Singular point perturbation of an odd operator in ℤ2-Graded space

Abstract

In the paper we study supersymmetric models for point interaction perturbations of operators of Dirac type and their spectral properties. Such models are considered in the class of odd self-adjoint operators in ℤ2-graded Pontryagin space. We present in detail the previously considered realization method of strongly singular perturbation by means of their embedding into the theory of self-adjoint extensions. We describe odd self-adjoint extensions of odd symmetric operators with deficiency indices (1,1) in ℤ2-graded Pontryagin space and squares of such extensions using Krein’s formula for the resolvent. The results obtained are refined in application to singular perturbations of odd self-adjoint differential operators.